Solving linear programming problems exactly

A linear programming problem in an inequality form having a bounded solution is solved error-free using an algorithm that sorts the inequalities, removes the redundant ones, and uses the p-adic arithmetic. (C) Elsevier Science Inc., 1997

Machine-tool selection and operation allocation in FMS: solving a fuzzy goal-programming model using a genetic algorithm

The decision-making process for machine-tool selection and operation allocation in a flexible manufacturing system (FMS) usually involves multiple conflicting objectives. Thus, a fuzzy goal-programming model can be effectively applied to this decision problem. The paper addresses application of a fuzzy goal-programming concept to model the problem of machine-tool selection and operation allocation with explicit considerations given to objectives of minimizing the total cost of machining operation, material handling and set-up. The constraints pertaining to the capacity of machines, tool magazine and tool life are included in the model. A genetic algorithm (GA)-based approach is adopted to optimize this fuzzy goal-programming model. An illustrative example is provided and some results of computational experiments are reported.

Computationally Efficient Sub-optimal Mid Course Guidance Using Model Predictive Static Programming (MPSP)

For a homing interceptor, suitable initial condition must be achieved by mid course guidance scheme for its maximum effectiveness. To achieve desired end goal of any mid course guidance scheme, two point boundary value problem must be solved online with all realistic constrain. A Newly developed computationally efficient technique named as MPSP (Model Predictive Static Programming) is utilized in this paper for obtaining suboptimal solution of optimal mid course guidance. Time to go uncertainty is avoided in this formulation by making use of desired position where midcourse guidance terminate and terminal guidance takes over. A suitable approach angle towards desired point also can be specified in this guidance law formulation. This feature makes this law particularly attractive because warhead effectiveness issue can be indirectly solved in mid course phase.

Register Allocation and Optimal Spill code Scheduling in Software Pipelined Loops using 0-1 Integer Linear Programming Formulation

In achieving higher instruction level parallelism, software pipelining increases the register pressure in the loop. The usefulness of the generated schedule may be restricted to cases where the register pressure is less than the available number of registers. Spill instructions need to be introduced otherwise. But scheduling these spill instructions in the compact schedule is a difficult task. Several heuristics have been proposed to schedule spill code. These heuristics may generate more spill code than necessary, and scheduling them may necessitate increasing the initiation interval. We model the problem of register allocation with spill code generation and scheduling in software pipelined loops as a 0-1 integer linear program. The formulation minimizes the increase in initiation interval (II) by optimally placing spill code and simultaneously minimizes the amount of spill code produced. To the best of our knowledge, this is the first integrated formulation for register allocation, optimal spill code generation and scheduling for software pipelined loops. The proposed formulation performs better than the existing heuristics by preventing an increase in II in 11.11% of the loops and generating 18.48% less spill code on average among the loops extracted from Perfect Club and SPEC benchmarks with a moderate increase in compilation time.

Minimization of Constraint Violation in Fuzzy Multiobjective Programming

Fuzzy multiobjective programming for a deterministic case involves maximizing the minimum goal satisfaction level among conflicting goals of different stakeholders using Max-min approach. Uncertainty due to randomness in a fuzzy multiobjective programming may be addressed by modifying the constraints using probabilistic inequality (e.g., Chebyshev’s inequality) or by addition of new constraints using statistical moments (e.g., skewness). Such modifications may result in the reduction of the optimal value of the system performance. In the present study, a methodology is developed to allow some violation in the newly added and modified constraints, and then minimizing the violation of those constraints with the objective of maximizing the minimum goal satisfaction level. Fuzzy goal programming is used to solve the multiobjective model. The proposed methodology is demonstrated with an application in the field of Waste Load Allocation (WLA) in a river system.

Optimum Load Shedding Through Programming Techniques

This paper obtains a new accurate model for sensitivity in power systems and uses it in conjunction with linear programming for the solution of load-shedding problems with a minimum loss of loads. For cases where the error in the sensitivity model increases, other linear programming and quadratic programming models have been developed, assuming currents at load buses as variables and not load powers. A weighted error criterion has been used to take priority schedule into account; it can be either a linear or a quadratic function of the errors, and depending upon the function appropriate programming techniques are to be employed.

Impact-Angle-Constrained Suboptimal Model Predictive Static Programming Guidance of Air-to-Ground Missiles

A nonlinear suboptimal guidance law is presented in this paper for successful interception of ground targets by air-launched missiles and guided munitions. The main feature of this guidance law is that it accurately satisfies terminal impact angle constraints in both azimuth as well as elevation simultaneously. In addition, it is capable of hitting the target with high accuracy as well as minimizing the lateral acceleration demand. The guidance law is synthesized using recently developed model predictive static programming (MPSP). Performance of the proposed MPSP guidance is demonstrated using three-dimensional (3-D) nonlinear engagement dynamics by considering stationary, moving, and maneuvering targets. Effectiveness of the proposed guidance has also been verified by considering first. order autopilot lag as well as assuming inaccurate information about target maneuvers. Multiple munitions engagement results are presented as well. Moreover, comparison studies with respect to an augmented proportional navigation guidance (which does not impose impact angle constraints) as well as an explicit linear optimal guidance (which imposes the same impact angle constraints in 3-D) lead to the conclusion that the proposed MPSP guidance is superior to both. A large number of randomized simulation studies show that it also has a larger capture region.